# Computer Simulation Resolves Critical Mixing Issue

*By Peter Hoffman,*** Hoechst Celanese Chemical Group, Inc.**

Would it be possible, in case of a problem, to mix a shortstop inhibitor into a monomer storage tank quickly enough to stop a runaway polymerization? The answer was important because if any hazard existed a considerable capital expenditure would be required to upgrade the tank. Testing this scenario with a scale model would taken months while plant management wanted to know whether the tank was safe immediately. Hoechst Celanese engineers solved the problem by using computational fluid dynamics (CFD) software to model the mixing process and found that the critical concentration of the inhibitor was achieved in 18 minutes—in plenty of time to stop the reaction.

The tank has a capacity of 243,000 gal (920 m^{3}) and the pumparound loop flowrate is 100 gal/min (0.0063 m^{3}/s). The critical concentration of inhibitor and consequently the amount of time available for mixing was defined by laboratory studies. In order to stop the runaway reaction, the inhibitor must be mixed to a 10-ppm concentration throughout the tank. A level of approximately 100 ppm will stop all polymerization. Depending on the temperature level and rate of temperature rise selected for starting the injection of the shortstop inhibitor, there is a window of between 1 and 6 h to achieve the required level of concentration.

*10 ppm isoconcentration surface at 2 minutes*
**Mixing** concerns

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The concerns about mixing the inhibitor arose partly because the turnover time for the tank is 40.5 hours. A second area of concern was that the eductors are located close to the floor of the tank and are aimed slightly below horizontal. It was not clear that there was sufficient vertical circulation in the tank. It was contemplated that modifications in the form of additional nozzles into the tank, internal sparger pumping and increased pumparound flowrate might be needed to achieve rapid enough mixed. At the very least, it was assumed that the existing eductor nozzles would have to be re-aimed.

Hoechst engineers felt that computational fluid dynamics (CFD) technology could solve this design problem. A CFD simulation provides fluid velocity, pressure and species concentration values throughout the solution domain for problems with complex geometries and boundary conditions. As part of the analysis, a researcher may change the geometry of the system or the boundary conditions such as inlet velocity, flowrate, etc. and view the effect on fluid flow patterns or concentration distributions. CFD also can provide detailed parametric studies that can significantly reduce the amount of experimentation necessary to develop a device and thus reduce design cycle times and costs.

**Software **selection

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Hoechst engineers selected Fluent CFD software from Fluent Inc. (Lebanon, NH) because it handles the widest range of applications of any CFD code, including multiphase flow, specialized chemistry, and multiple species transport. The user interface makes it easy to define a simulation. Conditions such as the type of combustion model, material properties, and turbulence are specified through the use of tables and drop-down menus rather than by entering information on a command line. In most cases, a user can be initiating an analysis in as little as 30 min after importing the analysis model or mesh.

The engineers made several assumptions about the problem for the purposes of the analysis. The inhibitor is dissolved in a solvent to a concentration of 10%. Sufficient inhibitor is injected so that the eventual uniform mixout concentration will be 1,000 ppm. The injection is via the pumparound loop, requiring about 25 min for completion with the existing pump. Another assumption is that the pumparound loop is running constantly so that the flow pattern in the storage tank is already established when the inhibition injection is triggered.

**Symmetrical **model

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The model developed by Hoechst engineers takes advantage of the symmetry of the storage tank to reduce the geometry to a half-cylinder. Engineers began by defining the boundaries of the geometry, then imposed a finite difference grid on the outside surfaces of the cylindrical tank. The eductors were modeled by the use of back to back inlet nodes, where the inlet node representing the suction side of the eductor was actually withdrawing material from the regime with negative flow. Another node represents the 4-in.-dia. exit from the eductor. The model used 24,360 nodes in the computational domain. The model of the tank was relatively simple yet still quite computationally intensive because it is three-dimensional and time-dependent in the calculation of concentration at each node.

The flow field was analyzed at steady state since the pumparound runs continuously. The first computational step was to get a converged solution for the steady-state flow field. At this point, the injection of the inhibitor solution was activated. The solution of inhibitor has an initial concentration of 100,000 ppm. The eductors are 3:1 mixers so that the jet issuing from the end of the eductor is 25,000 ppm. Sufficient inhibitor is injected in 25 min so that the eventual uniform mixout concentration is 1,000 ppm. The transient calculation of concentration was then performed with the velocity equations turned off.

*10 ppm isoconcentration surface at 16 minutes*
**CFD **results

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The results of the CFD modeling showed that the storage tank is in fact a very good mixing device. The critical concentration criteria of greater than 10 ppm of inhibitor was achieved everywhere in the tank less than 18 minutes after injection. This was graphically illustrated by Fluent plots that used an isoconcentration surface to divide the tank into two areas: one where concentration is above 10 ppm and the other where it is below. The less than 10-ppm volume shrinks in time and eventually disappears entirely.

As the analysis made clear, the main reason for the remarkably short period of time to reach the critical mixing concentration is that this requirement is not very stringent in terms of the usual mixing criteria. The usual mixing-time correlations are based on a close approach to uniformity, such as 95% to 99% uniform concentration. In this case, the requirement is to achieve a minimum concentration of 10 ppm, only 1% of mixout. It is roughly estimated that 95% uniformity would be achieved in approximately 1.5 to 2 h.

The primary lesson that can be learned from this analysis is that the information provided by computer simulation can often save time and expense. By providing a better understanding of a process, CFD can often eliminate the need to provide expensive and unnecessary testing and retrofitting.

*Edited by Nick Basta*

**About the author:***Peter Hoffman is a staff engineer at Hoechst Celanese Chemical Group, Inc., Corpus Christi, TX.*

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